# Implied expense theory in financial reporting: a steady-state approach

## Abstract

### Purpose

The purpose of this study is to use a steady-state model structure to investigate earnings management (EM) theoretically in the context of different expense theories. Empirically, the objective is to apply the theoretical model to investigate the implicit choice of expense theories for reporting expenses. The study aims to present a new approach to analyze EM.

### Design/methodology/approach

The study makes use of ten-year time-series data originally from 1,015 Finnish public and private firms to estimate the parameters of the steady-state model, and to investigate which expense theories the firms implicitly follow in financial reporting. The parameters are estimated using the restricted least squares regression method. The final sample included data from 631 firms fulfilling restrictions for the consistency of estimates.

### Findings

The paper provides empirical insights about expense theories that Finnish firms implicitly follow in financial reporting. Evidence shows that the reporting of expenses mainly follows the units-of-revenue and the rate-of-return theories. Only a small number of firms follow the interest expense theory.

### Research limitations/implications

The study is based on a steady-state approach, and therefore, the research results may lack generalizability as only 62% of the original sample firms obtained consistent estimates. Therefore, researchers are encouraged to use more general models for further theoretical and empirical work.

### Practical implications

The paper includes implications for a new approach to EM. It also gives implications how to analyze different expense theories in the context of EM both theoretically and empirically.

### Originality/value

This paper develops a new approach to investigate EM.

## Keywords

#### Citation

Laitinen, E. (2018), "Implied expense theory in financial reporting: a steady-state approach", *Journal of Financial Reporting and Accounting*, Vol. 16 No. 1, pp. 49-83. https://doi.org/10.1108/JFRA-05-2016-0032

### Publisher

:Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited

## 1. Introduction

Earnings are regarded as an important summary measure of a firm’s financial performance, and are often used in valuation and contracting (Bauwhede and Willekens, 2003), which enables managers to affect valuation and contracting by manipulating earnings. When managers use judgment in financial reporting and in structuring transactions to alter financial reports, either to mislead stakeholders about the underlying economic performance of the company or to influence contractual outcomes, they are engaging in earnings management (EM; Healy and Wahlen, 1999). EM has a negative impact on earnings quality and weakens the credibility of financial reporting. It leads to losses of investor wealth and misdirects resources from their most productive use (Beneish *et al.*, 2013). Thus, EM is an important issue for academics and practitioners, and a large body of academic research has examined the causes and consequences of EM. However, a central limitation of this line of research is that existing techniques for detecting EM lack power and are often misspecified (Dechow *et al.*, 2000).

There are many ways in which managers can exercise judgment in financial reporting. They can manage earnings by manipulating accruals (accrual manipulation) with no direct cash flow consequences or real activities (real activity manipulation) during the accounting period to meet certain earnings targets (Roychowdhury, 2006). Earnings are based on the difference between revenues and expenses. Therefore, managers can use EM to consider revenues and/or expenses. First, managers can manipulate revenues for example through premature recognition where revenues are recognized as sales before cash is collected (unearned revenues) using an aggressive or incorrect application of generally accepted accounting principles (GAAP; Stubben, 2010; Callen *et al.*, 2008). Second, managers can manipulate expenses by choosing from among various acceptable accounting methods to report the same economic transactions, such as the straight-line or accelerated depreciation methods or the last-in, first-out (LIFO), first-in, first-out (FIFO) or weighted-average inventory valuation methods (Healy and Wahlen, 1999). Such an approach is referred to in the accounting literature as within-GAAP earnings management (Bauwhede and Willekens, 2003). The present study does not deal with real activity or revenue manipulation and, instead, concentrates on the choice of acceptable accounting methods for reporting expenses; therefore, it belongs to the field of within-GAAP EM research.

The traditional methods for detecting EM are centered on accrual-based models using either time-series or cross-sectional data (Dechow *et al.*, 1995). The time-series models estimate nondiscretionary accruals from the past levels of the firm during periods when systematic EM is not assumed. Examples of such models include the Healy (1985), DeAngelo (1986), Jones (1991) and modified Jones (Dechow *et al.*, 1995) models. The cross-sectional models estimate the normal level of accruals in a period using accruals of comparable firms in the same period. The Jones cross-sectional model (DeFond and Jiambalvo, 1994) and the industry model (Dechow and Sloan, 1991) are examples of these kinds of approaches. The major problem for both approaches is that accruals vary with changes in business circumstances and growth. Therefore, a reliable benchmark is missing. The more recent models have sought to control for these changes with parameters adjusting accruals to these changes (Spohr, 2005, p. 17). However, practically all of the abovementioned techniques assume that the residual from a linear regression represents earnings management (Gerakos, 1967).

EM is closely connected to research in the relationship between the accounting rate of return (*ARR*) and the internal rate of return (*IRR*). In the present study, *ARR* is viewed as a (reported) proxy or surrogate for *IRR*, referring to the actual profitability (Luckett, 1984; Feenstra and Wang, 2000; Brief, 2013). Several early studies on this research area have analyzed the effect that different depreciation methods have on the reliability of *ARR* as a proxy of *IRR*. Harcourt (1965) argued that *ARR* is extremely misleading, even under ideal conditions. However, Solomon (1966) concluded that *ARR* equals *IRR* for different depreciation methods when *IRR* is equal to the rate of growth, while Vatter (1966) demonstrated that *ARR* always equals *IRR* when the annuity (compound interest) depreciation method is used. The structure of the models that researchers used was typically steady, and revenue (cash) flows generated by yearly investment expenditure were assumed to be separate to allow analysis of different depreciation methods. The objective of the present study is to use this kind of model structure to investigate EM theoretically in the context of different expense theories.

Empirically, the objective of this study is to apply the theoretical model to investigate the choice of accounting methods for reporting expenses. This empirical approach uses the time series of the firm to estimate a steady dynamic model of lagged revenue generation. These kinds of distributed lag models have earlier been used empirically to estimate *IRR* (Laitinen, 1997, 2006, 2012). This type of time-series approach is justified as earnings and accruals are best described by a firm-level dynamic process, and accruals are likely to be generated by a firm-level dynamic process (Gerakos, 1967). The present model enables us to estimate *IRR* and the parameter describing lagged revenue generation (revenue lag), which makes it possible to calculate the rate of expense according to different expense (depreciation) theories. The revenue lag provides us with a benchmark to assess timing of expenses. In this study, three kinds of expense theories are used to calculate this rate: units-of-revenue (proportional), rate-of-return (realization) and compound interest (annuity) expense theories (Saario, 1961; Bierman, 1961; Vatter, 1966; Wright, 1967). In practice, the application of different theories leads to different rates of expense for reporting the same economic transactions. Comparing these theoretically derived rates of expense with the actual rates makes it possible to find the (closest) theory implicitly followed by a firm and to estimate how much the choice of which theory to follow affects earnings.

The present study makes use of a large sample of Finnish industrial firms. Finland represents an excellent opportunity to investigate reporting practices. The 2008 global financial crisis produced a significant shock to the Finnish economy. The subsequent recession continued for years and changed the business environment of firms. This long-term recession led a significant number of Finnish firms to report negative figures for growth and profitability. Therefore, the Finnish data make it possible to obtain a sample with a very high variation in growth and profitability figures, which is important for EM research. The original sample consists of 1,015 private and public firms, each with a 10-year time series of financial statements extracted from the period between 2002 and 2015. However, the number of public firms is only 105 (10.3 per cent), owing to the small size of NASDAQ OMX Helsinki. The type of firm (private or public) does not affect the application of the approach as the parameters are estimated for each firm separately. The Finnish GAAP (following the 2004 reform of Accounting Act 1304/2004) are quite flexible, allowing a wide variety of acceptable methods for reporting depreciations and current expenses (Sundgren, 2007; Pajunen, 2010). However, in early 2005, the international financial reporting standards (IFRS) became obligatory for the consolidated reports of public companies, which meant that public and private companies did not follow the same accounting laws and regulations. In the original sample, only two private firms report having voluntarily adopted IFRS. Sundgren (2007) found no significant differences in the accounting choice between public and private companies from 1997-2001, while Spohr (2005) questioned whether public firms engage in income smoothing at all. The time series of the present study are extracted from the period 2002-2015, which does not overlap with the abovementioned EM studies.

The remainder of this paper is structured as follows. Section 1 presents the motivation and objective of the study. Section 2 will present the analytical framework for the steady distributed lag model and for the three expense theories. Furthermore, at the end of the section, five research hypotheses will be derived between the characteristics (*IRR* and the revenue lag) of the firm and the choice of the expense theory. Section 3 introduces the empirical sample and statistical methodology. The restricted least squares method based on the Koyck transformation acts as the main statistical method. Because of the strict assumptions of the steady framework, many of the firms did not get allowable estimates. Therefore, the final sample only included 631 firms. Section 4 presents empirical results, while Section 5 summarizes and discusses the findings.

These findings generally show that for the 10-year period, 43.6 per cent of the firms can be considered followers of the units-of-revenue expense theory, where expiration of expenditure follows the lagged revenue distribution. However, 53.4 per cent of the firms follow the rate-of-return theory, which also allows *IRR* to adjust the rate of expense. The compound interest theory is rare and only followed by 3.0 per cent of the firms. Thus, the results imply that more than 50 per cent of Finnish firms implicitly use a smoothing mechanism in financial reporting. The results also implicate that reported *ARR* is typically not a reliable proxy for *IRR* as very few firms follow the compound interest expense theory that makes *ARR* equal to *IRR*, and *IRR* rarely equals the growth rate. However, the average bias is not strong owing to low average *IRR* and growth rate during the research period suffering from a recession. In summary, the new approach used in this study proved promising for analyzing EM.

## 2. Framework of the analysis

### 2.1 Theoretical background

The expense behavior of firms in financial reporting is here analyzed using different expense theories that have a different view of reported earnings. These expense theories will be drawn here analytically using a similar framework to that which researchers use to analyze the relationship between the reported *ARR* or the return on investment (*ROI*) ratio and the *IRR*. *IRR* is the central concept of profitability that economists use when discounting cash flows and it is called the economic rate of return (*ERR*; Feenstra and Wang, 2000; Brief, 2013; Luckett, 1984). This body of research is strongly motivated by EM. GAAP gives managers a lot of discretionary power (regarding inventory valuation, depreciation, R&D expenses, etc.) which can yield measurement errors of *ARR*. When comparing the annual *ARR* with *IRR*, researchers usually address the issue of whether a periodic *ARR* serves as a reliable measure of constant *IRR*. This previous research concludes that the reported *ARR* is generally a very poor proxy for *IRR* (Feenstra and Wang, 2000). The models used in this research area are, however, useful in depicting alternative accounting methods. The present study makes use of a similar model structure.

The models of early researchers analyzed the effects of the length of project life, cash flow pattern, growth rate and accounting method with respect to the capitalization and depreciation of investment outlays that would affect the relationship between *ARR* and *IRR* (Harcourt, 1965; Solomon, 1966; Kay, 1976; Fisher and McGowan, 1983; Whittington, 1988; Peasnell, 1982, 1996). The present framework uses similar concepts in the following manner. The framework analyzes the revenue flows at the level of the firm (instead of a project); thus, the length of project life is assumed to be infinite, simplifying the model considerably. The cash flow (revenue) pattern is described here by a geometric lag structure between total periodic expenditure and the generated flow of total revenue (net sales). The geometric lag structure is justified as the greater part of total expenditure is consisted of current expenditure-generating revenues, either immediately or very quickly. This revenue lag structure is important in differentiating between firms from different industries that have different revenue lags. The parameter of the lag distribution describes the form of the structure and the length of the lag and, thus, reflects the timing of revenues. For simplicity, the present framework makes a steady-state assumption, leading to the growth rate being identical for all accounting concepts (expenditure, revenue, expenses and assets). This is a general assumption of the models applied on this area of research (Feenstra and Wang, 2000; Luckett, 1984).

The model structure is simple but useful for depicting different expense theories (accounting methods). The matching principle (convention) is one of the most common underlying guidelines in accounting. It is also one of the most controversial conventions in different expense (income) theories (Brief, 1993). Moreover, it is a central means of EM (Sun and Rath, 2010). The matching principle requires firms to report expenses on their income statement in the same period as related revenues. If expenditure generates a flow of revenue over many periods, this expenditure should be allocated to its life as expenses matched with related revenue contributions. Theoretically, this matching (time allocation) process requires the revenue contributions generated by successive periodic expenditures to be both known and separable. This separability makes it possible to trace back the periodic expenditure that has generated a certain piece of revenue (contribution) in a period. Different theories have different ways of understanding how this piece of revenue can be used in matching. In the present study, three different theories are used to describe the allocation of expenditure over time: units-of-revenue, rate-of-return and compound interest expense theories (Saario, 1961; Bierman, 1961; Wright, 1967). If the revenue lag structure is level, the units-of-revenue theory leads to a neutral expense pattern over time, while the rate-of-return theory leads to an accelerated pattern and the compound interest theory to a decelerated pattern. Thus, these three theories form a representative sample of expense theories with respect to time allocation. The present approach differs conceptually from the previous models as it is based on expenditure, revenue, assets and expense concepts instead of fixed expenditure, gross profit, fixed assets and depreciation. Therefore, the concept of depreciation theory is replaced here with the concept of expense theory.

### 2.2 Rate of expense

The present model of the firm is based on a simplified steady-state framework for investigating analytically different expense theories. Thus, it is first assumed that the rate of expense *p* is constant over time. The (total) expense of period *t C* (*t*) is defined as follows:

*A*(

*t*) and

*E*(

*t*), respectively, refer to (total) assets and (total) expenditure in period

*t*. This framework is based on the concept of total expense, including both current expense and depreciation. Therefore, it is preferred to use the concept of expense theory rather than the more limited depreciation theory. Similarly, a broader concept of total assets is used hereafter instead of fixed assets. The concepts of fixed assets and depreciations are generally used in steady accounting models built to investigate reporting of

*ARR*(Feenstra and Wang, 2000; Brief, 2013).

The accounting identity between expenditure and expense concepts tells the following:

Which, together with equation (1), leads to:

*g*is the steady growth rate of total assets. Equation (3) shows that the constant relation between total expenses and total expenditures depends on the rate of expense

*p*but also on the rate of growth

*g*.

### 2.3 Distributed lag model of revenue

Many expense (depreciation) theories are revenue-based and recognize the relation between revenue and expenditure to draw expense. This relation is described in the present study by a steady-state model based on assumptions of identical investments (Laitinen, 2006, 2012). This kind of general framework has been used to analyze the association between *ARR* and *IRR* (Feenstra and Wang, 2000; Brief, 2013). More specifically, the present model assumes that each periodic expenditure *E*(*t*) generates proportionally identical and separate flow of revenue converging geometrically at a constant rate *q* toward infinity. Each unit of expenditure is expected to generate *M* units of revenue. Therefore, *M* is referred to here as the monetary productivity of expenditure measured in units of revenue. The *IRR* of expenditure *E(t) r* can be extracted from the following identity:

*q*/(1 +

*r*) < 1 and

*q*< 1. In equation (4),

*q*measures the time lag between expenditure and the flow of revenue and is referred to here as the revenue lag. The average time lag of the geometrically distributed infinite lag function is

*K*=

*q*/(1−

*q*).

*K*is an increasing function of

*q*.

The standard steady-state framework assumes that expenditure *E(t)* will grow at a constant rate *g* over time. Therefore, total revenue *R(t)* realized in period *t* can be expressed as the sum of revenue contributions generated by past and current expenditures as follows:

*q*/(1 + g) < 1 and

*q*< 1.

*F*is the revenue–expenditure ratio, which refers to the degree of revenue finance in expenditure.

*F*is symmetrical with respect to

*r*and

*g*. Thus,

*F*equals unity when

*r*=

*g*and exceeds unity when

*r*>

*g*. It is increasing in

*r*and decreasing in

*g*.

Equations (2), (3) and (5) enable us to derive *ARR* or the *ROI* defined on the beginning-of-period basis, as follows:

Equation (6) shows that the relation between *ROI* and *r* is quite complicated and depends on the growth of the firm (*g*), the revenue lag (*q*) and the expense theory adopted (*p*). However, when *g* = *r*, *ROI* = *r* irrespective of *q* or *p*. This is a general result in a steady (Golden Age) framework (Solomon, 1966).

### 2.4 Different expense theories

#### 2.4.1 Units-of-revenue (proportional) expense theory.

The present study applies three different expense theories to draw the rate of expense (see Laitinen, 2012). First, the units-of-revenue (proportional) expense theory, leading to a neutral expense pattern is considered. This theory follows the concepts and philosophy adopted in accounting practice when applying, for instance, the units-of-production expense method, in which expense varies in a direct proportion to usage of assets leading to a simultaneous recognition of revenue and expense. This kind of method is consistent with the IASB, where expenses are recognized in the income statement when a decrease in future benefits related to a decrease in an asset has arisen that can be measured reliably (IASB Framework, paragraph 94). In practice, the units-of-revenue theory is one of the most accurate expense methods for matching expenses with revenue, but requires careful tracking of asset usage and the ability to estimate total usage over the life of the asset.

In the annual closing of the books, periodic expenditures are classified into two categories: expenses (expired expenditures) and unexpired expenditures. The unexpired expenditures have until the end of accounting period not yet generated revenues and they will be added to the assets of the firm. The units-of-revenue, or proportional expense, follows this line of thinking and assumes that the assets of the firm consist of the proportional part of expenditures, which is to generate revenues in the future. Thus, this theory does not apply present values or discounting; instead, it follows the units of revenue generation expired during the accounting period. The assets of the firm using this expense theory depend directly on the revenue contribution distribution. These assets can be determined by summing up the unexpired proportions of periodic expenditure to infinity, as follows:

*IRR*(

*r*), but is decreasing in

*g*and increasing in

*q*.

The accounting identity between expenses and expenditures makes it possible to calculate total expense *C*(*t*) from equation (7), as follows:

*p*. Thus,

*p*is directly related only to the accumulation of revenue over time or to the revenue lag (

*q*). The units-of-revenue expense can therefore be regarded as a neutral expense method.

When *ROI* is defined on the beginning-of-period basis, the use of this expense theory leads to the following relationship between *IRR* and *ROI*:

On using equations (5), (7) and (8). Thus, *ROI* is biased and increasing in the rate of growth *g*, and equals *r* only if *r* = *g*.

#### 2.4.2 Rate-of-return (realization) expense theory.

Second, the rate-of-return or realization theory of expense is considered. This theory is strictly associated with the revenue flow generated by expenditure (Saario, 1961; Bierman, 1961). It suggests that it is necessary to view the purchase of an asset as an acquisition of a series of revenue-generating services, rather than as a purchase of a physical unit. Therefore, expenses are determined by the present value of realized revenue, discounted by *IRR* to the moment of acquisition. This present value is regarded as the purchase price (expense) of the revenue realized. In the case of a level contribution (revenue flow) distribution, adopting the realization theory leads to an accelerated depreciation pattern. For this reason, Järvinen (1967) recommended this theory as the basis of tax neutral expense in Finland, but concluded that it is difficult to apply in practice owing to the assumptions of separability of revenue and perfect certainty (information). The IASB (IFRS, 2013) proposes that a revenue-based depreciation (expense) method should not be applied under IFRS because it reflects a pattern of economic benefits being generated from operating the business (of which the asset is part) rather than the economic benefits being consumed through the use of the asset (Paragraph 60 of IAS 16).

This expense theory assumes that expenses are calculated by discounting each revenue contribution realized in a period to the period (moment) of investment up to infinity. Thus, expenses are determined as follows:

Which leads to the following rate of expense when equation (11) is set equal to equation (3):

Thus, the rate of expense in financial reporting is dependent on the revenue lag (*q*) but also on *IRR* (*r*).

The accounting identity equations (8) and (11) together show that the assets of the firm can be presented as follows:

Which leads to the following expression of *ROI*:

Thus, the *ROI* is biased and the relation between *IRR* and *ROI* is proportional to the revenue–expenditure ratio (5) leading to *ROI* = *r* only when *r* = *g*.

#### 2.4.3 Compound interest (annuity) expense theory.

The third expense theory used in this study is the compound interest or annuity method (of depreciation), presented by Ladelle in 1890 (Wright, 1967). This theory is based on the economic wealth assumption, according to which the financial position of the firm is related to its future revenues. Consequently, the assets of the firm are determined as the present value of future revenues generated by past and present expenditures, and that will be realized in the future. In the present value, the *IRR* is used as the rate of discount. Thus, the purchase price of an asset is equal to the present value of its expected net services. The periodic profit is measured as the increase in the present value of assets over the period. The revenues are assumed to consist of two parts. The first part is the return on investment and the second part is the depreciation. The share of the depreciation will increase with the passage of time; in the case of a level revenue flow (contribution) distribution, this will lead to a decelerated depreciation pattern. This expense (depreciation) theory is widely appreciated by researchers in the field (Brief, 1993). However, the IASB proposition that a revenue-based (depreciation) method should not be applied under IFRS also holds for the annuity expense method (IFRS, 2013). Therefore, IFRS is of the considered opinion that annuity method under IFRS is not an appropriate (depreciation) method. It is only rarely adopted in practice (Bragg, 2010, p. 198).

When the firm applies the annuity expense theory, the assets are determined as the present value of future revenues generated by past and present expenditures and that which will be realized in the future. This leads to the following result:

Substituting equation (15) into equation (2), the periodic expenses are obtained as follows:

When equation (3) is set equal to equation (16), the rate of expense *p* can be presented in the following form:

Which depends also on the rate of growth *g* in addition to *IRR* and *q*.

Equations (5), (15) and (16) together give the following expression for *ROI*:

Showing that *ROI* or *ARR* is unbiased and exactly equal to *IRR* when the compound interest expense theory is applied in financial reporting (Vatter, 1966).

### 2.5 Hypotheses

The modeling in this study is based on a simplified steady-state framework. Three kinds of expense theories are considered to give a description of the rate of expense *p*. It is not argued that firms consciously use these kinds of theories in practice but merely that they act as though they were doing so in financial reporting, leading to a rate of expense proposed by such theory. Therefore, an expense theory may be vindicated even if firms do not explicitly and consciously act in accordance with its assumptions. Thus, the theory behind this kind of behavior can be called implicit expense theory. Expense information is crucial in financial statements for measuring the financial performance of the firm and *ARR* or *ROI* plays the central role in this measurement. Previous studies have indicated that different methods to depreciate (fixed) expenditures obviously lead to different reported *ROI* figures (Luckett, 1984; Feenstra and Wang, 2000; Brief, 2013). *ROI* figures may be seriously biased owing to differences in growth, revenue lag distribution and investment project duration between reporting firms. Thus, the general conclusion is that *ARR* is not an accurate measure of *IRR* and that the measurement error in *ARR* is neither constant nor consistent (Solomon, 1966).

Previous studies have concentrated on the relationship between *ARR* and *IRR* to assess the accuracy of ARR as a proxy of *IRR*. They have not directly given any evidence for the present hypotheses on the potential followers of different expense theories in EM. However, the findings could be used to give indirect evidence. For example, Vatter (1966) concluded that the use of the compound interest depreciation leads to *ARR* = *IRR* under any circumstances, which is consistent with equation (18). This result could imply that this depreciation is used by profitable firms without any special pressure for EM. Solomon (1966) showed that under certain circumstances, the straight-line depreciation leads to *ARR* higher than *IRR* and that the sum of the years’ digits (SYD) depreciation gives even higher *ARR*. Therefore, one could expect that firms with low profitability would prefer to use these depreciation methods to increase reported *ARR*. This kind of indirect analysis could be conducted also for the straight-line, SYD and the double-declining balance depreciations on the basis of the results reported by Buijink and Jegers (1989). For the present analysis, these kinds of assumptions can be derived from equations (10), (14) and (18). However, this study adopts a different viewpoint. The use of the compound interest method as a benchmark for a neutral depreciation has not been well empirically justified as this depreciation is not considered an appropriate method under IFRS and is very rarely explicitly adopted in practice (Bragg, 2010, p. 198). Therefore, the units-of-revenue method, in which accumulation of expenses exactly follows accumulation of revenues, is regarded here as the neutral depreciation. Finally, the hypotheses in this study will be derived by focusing on the rate of expense, rather than on the relationship between *ARR* and *IRR*.

The units-of-revenue (or proportional) expense theory is based on the simultaneous recognition of revenue and expense, being a representative of an accurate and a neutral expense method. It is an expenditure-based expense method as it is independent of absolute revenue, although it is timely following the revenue lag distribution. The use of this theory leads to reported *RO*I (calculated on a beginning-of-year basis) being higher for firms exhibiting a higher rate of growth *g*. If the growth of rate is lower than *IRR*, *ROI* underestimates *IRR*. It also leads to the rate of expense *p ^{p}* = 1-

*q*being dependent only on the revenue lag, thus providing us with a benchmark for timing of expenses. It is expected that firms use this kind of neutral method without any special pressure to increase or decrease reported profits through EM. Thus, the following general

*H1*is presented for the users of this expense theory:

*H1.*

Firms following the units-of-revenue expense theory tend to exhibit average profitability.

The rate-of-return expense theory is a revenue-based method that refers to the discounted value of realized revenue as the periodic expense. When a firm implicitly follows this theory, the resulted *ROI* is biased, being a multiplicative function of the revenue–expenditure ratio *F* and *IRR*. If *IRR* exceeds the rate of growth *g*, *ROI* is higher than *IRR*, and vice versa. In financial reporting, this theory states that the rate of expense will be *p ^{r}* = 1−

*q*/(1 +

*r*), depending on

*IRR*in addition to the revenue lag

*q*. It is an increasing function of

*IRR*and

*p*=

^{r}*p*only if

^{p}*r*= 0. Therefore,

*p*>

^{r}*p*when

^{p}*r*> 0 and

*p*<

^{r}*p*when

^{p}*r*< 0. Thus, the theory includes a smoothing mechanism that in financial reporting increases the rate of expense for a positive

*IRR*and decreases it for a negative

*IRR*.

However, it is realistic to assume that accounting legislation and GAAP set limits for the mechanism that quite strongly affects the reported rate of expense. First, let us assume that the reported rate of expense is below a predetermined limit *MAX* (*r > 0*) and above a limit *MIN* (*r < 0*) in a relation to the neutral rate of expense 1-*q*. The range between *MIN* and *MAX* can be called the expense management flexibility limits (Choy, 2012). The nature of business and operating activities determine the set of GAAP applicable to the firm. The governance structure and both the internal and external monitoring mechanisms affect the choice of accounting methods from the menu of acceptable methods set by GAAP. These factors determine the allowable set of expenses and set the flexibility limits of a firm.

In this case, the rate of *IRR* is limited to the following range:

When *MAX* is only slightly exceeds 1 and *MIN* is only slightly below 1 (a limited EM opportunity), the potential range of *r* is limited on a narrow area around the origin. For a high positive *r*, the resulted *p ^{r}* exceeds the upper limit set by

*MAX*; for a low negative

*r*,

*p*falls below the lower limit set by

^{r}*MIN*. Therefore, the following is hypothesized:

*H2.*

Firms following the rate-of-return expense theory tend to exhibit either positive or negative profitability close to zero.

When *r* is restricted on a narrow area around the origin, it also restricts the allowed range of *q* for a rate-of-return expense theory. The relation between *MAX*, *MIN*, *r* and *q* can be solved as an equation form for *q*, as follows:

If *r* is distributed on a narrow area around the origin, *q* must be quite high to fulfill equations (20) for both positive and negative *r*. Thus, the following hypothesis is presented:

*H3.*

Firms following the rate-of-return expense theory tend to exhibit a high revenue lag.

The compound interest (annuity) expense theory is a revenue-based method that refers to the expense as the difference between periodic revenue and *ROI*. This theory is beneficial from the perspective of profitability measurement as it leads to the unbiased *ROI* so that *ROI* = *r*. However, the rate of expense is a quite complicated function of *q*, *r* and *g*, as shown by equation (17), recalled here:

This rate of expense *p ^{a}* is higher than the neutral rate 1-

*q*when

*r*> 0 and lower when

*r*< 0. Thus, it includes a similar smoothing mechanism to the rate-of-return expense theory. For the three expense theories, the rates are equal to 1−

*q*when

*r*= 0.

However, the rate of expense *p ^{a}* is lower than

*p*when

^{r}*r*> 0 and higher than

*p*when

^{r}*r*< 0. Thus, the smoothing mechanism with respect to

*IRR*is not as strong as for the rate-of-return expense theory. However,

*p*increases in

^{a}*g*when

*r*> 0 and decreases in

*g*when

*r < 0*. Thus, the growth of the firm makes the smoothing mechanism stronger, being weaker than for the rate-of-return expense theory. If

*g*= 0, then

*p*= 1−

^{a}*q*/(1 +

*r*(1−

*q*)). If the firm reaches

*MAX*or

*MIN*(in relation to the neutral expense rate 1-

*q*) as a predetermined level in EM,

*IRR*fulfils the following condition:

When equation (22) is compared at the limit values *MAX* and *MIN* with (19), it can be seen that the compound interest expense theory leads at *MAX* to a higher *IRR* than the rate-of-interest expense theory when *r > 0* and to a lower *IRR* when *r < 0*. This result is obvious as

Thus, the following hypothesis is presented:

*H4.*

Firms following the compound interest expense theory tend to exhibit either higher positive or lower negative profitability than the followers of the rate-of-return expense theory

When the relation between *r* and *q* is explicitly considered for the compound interest expense theory, the result is mathematically complicated. However, this relation can be presented at *MAX* and *MIN* in the following implicit form:

This implicit result shows that if the absolute value of *r* is high (*r* being either positive or negative figure), *q* tends to be low. Thus, the following hypothesis is presented:

*H5.*

Firms following the compound interest expense theory tend to exhibit a lower revenue lag than firms following the rate-of-return expense theory.

## 3. Empirical data and methods

### 3.1 Empirical background

There are a number of different empirical approaches in detecting earnings. Sun and Rath (2010) classified these studies as dealing with changing accounting choice, real transactions, total accruals/discretionary accruals, specific accruals, earnings distributions and income smoothing. The present study is related to changing accounting choice and total accruals/discretionary accruals approaches, which are reviewed briefly below. The objective of specific accruals approaches is to provide an efficient control for variables, concentrating on industries where a specific accrual is significant. The present study adopts a general approach and is not connected to any specific industries or accruals. Moreover, this study does not deal with real transactions and is, therefore, not related to that approach. The income-smoothing approach is useful for detecting EM through the temporal volatility of earnings, whereas the earnings distribution approach can be used in detecting benchmark-beating behavior. However, these approaches to detect EM are also outside the scope of the present study.

Studies on accounting choice have mainly been based on the positive accounting theory, which suggests that managers will show opportunism and choose accounting method that leads to the maximization of their personal wealth (Watts and Zimmerman, 1978). These studies have sought to detect the aggregate influence of accounting choices on financial reporting using a binary or categorical variable to capture income-increasing or income-decreasing EM. This approach is appealing as accounting choice can have a material effect on reported earnings and this choice can be observed by a discretionary measure. For example, Christie and Zimmerman (1994) classified accounting choices into an income-increasing strategy and an income-decreasing strategy and tested these on a sample of firms, separately using a multiple regression that controls for efficient choice of accounting methods. They concluded that while some accounting opportunism exists, efficiency is the more important explanation of accounting choice.

Total accrual/discretionary accrual approaches are based on the accrual components of earnings. The mainstream of these approaches have concentrated on the discretionary part of total accruals, which are adjustments to cash flows selected by the managers within the flexibility of accounting regulations, providing an opportunity to manipulate earnings (Dechow, 1994). The main challenge in research is that the components of total accruals are unobservable, which makes it difficult to estimate the discretionary part. Healy (1985) used total accruals as a proxy for discretionary accruals, assuming that the expected value of non-discretionary accruals equals zero. DeAngelo (1986) assumed that the average change in non-discretionary accruals is approximately zero, which means that a significant average decrease in total accruals primarily reflects a significant average decrease in discretionary accruals.

However, it has been argued that the level of non-discretionary accruals should change periodically as a response to changes in economic environment (Kaplan, 1985). Thus, these approaches tend to detect EM erroneously. Therefore, Jones (1991) applied a linear time-series regression equation with change in sales (current expense) and property, plant and equipment (depreciation expense) to control for nondiscretionary determinants of accruals. Later, Dechow *et al.* (1995) introduced a cross-sectional regression model as the modified Jones model. In that model, revenue is adjusted for change in receivables in the event period. Kothari *et al.* (2005) improved the performance of the approach using the residuals from the same-industry firms matched on profitability (*ROA*). In these models, the residual from a linear regression of total accruals represents EM. However, McNichols (2000) argued that the measures based on the Jones model or the modified Jones model are not sufficiently powerful or reliable to assess earnings management behavior when partitioning variables are correlated with earnings growth.

The present study is related to the above empirical approaches. It deals with the accounting choice approach because the objective is to investigate different expense theories that managers have implicitly chosen to follow in financial reporting. Each expense theory leads to different earnings for the same economic transactions. However, the present approach differs from previous studies in that the choice of accounting method is not considered explicitly, and is instead implicitly assessed on the basis of financial reporting. This study is also closely related to the accruals approaches (total accruals/discretionary accruals approach). Expense theories are based on matching expenses with revenues and the accounting system creates accruals to recognize revenues when they are earned and match expenses to those revenues (Sun and Rath, 2010). However, this study deals with accruals from a point of view different from the previous accrual EM approaches.

Virtually all previous accrual techniques have assumed that the residual from a linear regression of total accruals represents earnings management (Gerakos, 1967). The major problem for these approaches is that accruals vary with changes in business circumstances and growth. Recent models have attempted to control for these changes with parameters that adjust accruals to these changes (Spohr, 2005, p. 17). However, a reliable benchmark for the normal level of accruals is still missing, although cross-sectional, time-series and matched sampling techniques have been adopted. The present approach does not directly estimate accruals but, instead, uses the time series of a firm to estimate the dynamic revenue generating process. These kinds of time-series analyses have been used previously for estimating *IRR* for a firm (Laitinen, 1997, 2006, 2012). This approach is justified as earnings and accruals are best described by a firm-level dynamic process and accruals are also likely to be generated by a firm-level dynamic process (Gerakos, 1967).

The advantage of the present analysis is that the estimation procedure gives an estimate of the lagged revenue distribution of the firm. This function can be described by *IRR* and the lag parameter referring to the temporal distribution of lagged revenue contributions. When these separate revenue contributions are estimated, it is possible to match expenses with revenue to create accruals in many ways using different expense theories. Thus, the estimated revenue lag parameter provides us with a benchmark to assess timing of expenses and to create accruals. In this study, three kinds of expense theories are used to create accruals: units-of-revenue (proportional), rate-of-return (realization) and compound interest (annuity) expense theories. The application of different theories leads to different rates of expense. When these derived rates of expense are compared with the actual rates, it is possible to find the (closest) theory implicitly followed by a firm, and to estimate how much the decision to follow a certain theory affects reported earnings.

In this study, the estimation of the model is carried in two separate stages. First, the steady growth rate *g* is estimated using an ordinary least squares method. Second, a restricted least squares method is used to estimate the parameters *q* and *r* for the distributed lag model of revenues, using the estimated growth rate *g* as a restriction. These parameters make it possible to calculate the rate of expense according to the theories. The most challenging task in this approach is how to estimate reliably the distributed lag model from a relatively short time series (Hall, 2007).

### 3.2 Original empirical data

The present model is based on simplified assumptions related to a steady state and steady long-term growth. Therefore, empirical data are gathered from firms that fulfill a minimum size limit and have a longer time series of successive financial statements available. Very small firms usually exhibit an unstable development that is not consistent with steady assumptions. Therefore, the empirical data of the study are extracted from the ORBIS database of Bureau Van Dijk (BvD) under restrictions that the selected firm must be Finnish, must have financial statements available for at least 10 successive years and must have employed at least 50 employees in each year. A number of other restrictions are also considered later. ORBIS is a commercial database that contains administrative information on nearly 170 million companies across the globe. More than 99 per cent of the companies covered in this database are private companies.

Originally, 1,015 firms met the above three criteria. Table I presents descriptive statistics of the development of the number of employees in the firms. The average number of employees is approximately 1,000, whereas the median number is only close to 200. The size distributions in each year show a high skewness and a high kurtosis. The last financial year available varies between 2011 and 2015 in a manner that the great majority of firms have financial statements until 2014 (908 or 89.5 per cent) or 2015 (62 or 6.1 per cent). On average, the growth of the sample firms has been slow or even negative. This development is because of the 2008 global financial crisis. This crisis first touched the US financial sector in 2007, but the effects spread to several national economies, resulting in what has often been called the Great Recession. Appendix 1 presents Finnish macroeconomic indicators for the research period. These indicators show that the economic development in Finland has been unstable and quite negative. Thus, this period may, to some degree, distort the assumption of steady growth, although it still offers an opportunity to analyze expense behavior under conditions of negative growth and profitability. Usually, a steady framework only considers positive growth and profitability. However, the results of this study based on steady assumption should be interpreted with caution owing to the instability of the period.

The sample firms are from different industries, but the majority of firms have concentrated on few industries. Three hundred and ninety-three (38.7 per cent) firms were from the manufacturing industry, 177 (17.4 per cent) from wholesale and retail trade, 71 (7.0 per cent) from professional, scientific and technical activities, 65 (6.4 per cent) from information and communication and 64 (6.3 per cent) from construction. The sample mainly consists of 971 (95.7 per cent) industrial firms and 37 (3.6 per cent) financial companies. The legal forms of the firms are mainly private limited (881; 86.8 per cent) and public limited (105; 10.3 per cent) companies. Finally, the most frequent status in the sample is active (950; 93.6 per cent), dissolved (53; 5.2 per cent) and bankrupt (7; 0.7 per cent) firms. The advantage of the present approach is that it is general and can be applied to all types of firm. This is important especially when analyzing private firms following local GAAP and public companies following IFRS in financial reporting. However, the potential differences in implied expense theory between the types are interesting and are analyzed later in the study.

### 3.3 Statistical methods

The most challenging issue in statistical analysis is the estimation of the parameters of the steady-state model, which are *g*, *q* and *r*. First, the steady model assumes that all time-series are growing at the same steady rate of growth, *g*. The most important time series are those of total revenue *R(t)* and total expenditure *E(t)*. Total revenue is measured here by net sales and total expenditure by the sum of current expenditure and fixed expenditure (investment expenditure). The last nine observations are only available for estimation as total expenditure is calculated as the sum of total expenses and change in inventories and fixed assets. For both nine-year time-series, the steady growth rate *g* is estimated from the following assumed relation using the ordinary least squares (OLS) method:

*ε*is a random residual. As the estimates of

*g*for

*E(t)*and

*R(t)*usually differ from each other in practice, the final estimate of firm-level steady growth is calculated as the weighted average of these estimates using the sum of time-series over nine observations as weights.

Second, it is very challenging to reliably estimate *q* and *r* owing to the sensitivity of estimates (Laitinen, 1997; Hall, 2007). These parameters are here estimated using the Koyck transformation applied to the distributed revenue lag function. Furthermore, linear restrictions are incorporated in the estimation to make the estimates more stable (Johnston, 1972, pp. 155-159; Fomby *et al.*, 1984, pp. 82-85). The variance of the restricted estimators is lower than that of the unrestricted ones. The Koyck transformation shows that the relations (4) and (5) between *R(t)* and *E(t)* can be presented in the form of the following equation:

*a*is to be set equal to 0,

*A*= (1 +

*r*−

*q*)/(1 +

*r*) and

*ε*is a random residual. Note that

*A*=

*p*as it is presented in (12).

^{r}The central linear restriction is based on the relation (5) describing the revenue-expenditure ratio *F*. Because *F* = *A*·(1 + *g*)/(1 + *g*−*q*), there is the following relation:

These restrictions can be presented in the matrix form as ** h** =

**, where**

*H·B***is the 3 × 1 matrix of estimates. In these restrictions, the estimates of**

*B**g*and

*F*were used to stabilize the estimates of

*q*and

*r*.

*F*is estimated as the ratio of the sum of revenue and the sum of expenditure over the period of nine observations. Statistical experiments showed that the incorporation of linear restrictions in the model is essential to the reliability of the model estimates.

### 3.4 Testing hypotheses

The robustness of the results is important to the present study based on long-term analysis of quite unstable time-series. Therefore, the steady models are also estimated for a shorter period of seven first years. The results for this shorter period and for the initial longer period are compared with each other to assess robustness. When the results are estimated for two different successive periods, it also provides us with an opportunity to analyze the change in expense behavior in last years. Because the time-series are overlapping and the change period only covers two years, it is expected that the change is not remarkable, but is identifiable anyway. Thus, the five hypotheses are separately tested for the two periods and the results are compared with each other. Furthermore, the transitions from one expense theory to another during the change period are used to assess the stability of classification.

The steady-state model presented in this paper is based on many logical and convergence assumptions. If the estimates of the parameters are not consistent with the assumptions, it is not reasonable to draw conclusions about the expense theory implied by evidence. Therefore, only the firms that fulfill the minimum technical criteria and also the criteria set for the type, legal form, and status were selected from the original sample for further analyses. Panel 1 of Table II presents the number of firms fulfilling these criteria. On average, 933 (92.9 per cent) out of 1,015 firms fulfill the criteria when they are considered individually. The most limiting criterion is the positivity condition for *q* (*q* > 0), which was violated by 12.2 and 14.3 per cent of the firms for the periods of nine and seven years, respectively. Panel 2 presents the total number of criteria fulfilled by the sample firms. In further analyses, the final sample in which the hypotheses are to be tested is limited to the set of firms fulfilling all 17 criteria. The panel shows that the number of these firms in the final sample is 631 (62.2 per cent). Thus, 384 (37.8 per cent) firms included in the original sample are excluded from the final sample.

The rates of expense implied by the three theories are calculated for the estimated values of parameters using equations (9), (12) and (17), respectively. The actual rate of expense is defined following (1) in the way that total annual expense (current expense and depreciation) is divided by total annual expenditure (current expenditure and long-term expenditure) and assets (inventories and fixed assets) in the beginning of the year basis. The final (weighted) rate is calculated by dividing the sum of expenses by the sum of expenditure and assets over the research periods of nine and seven years. Then the absolute difference between the actual rate of expense and the rates implied by the theories are calculated as follows:

*p*is the actual rate of expense. Here, the firm is said to implicitly follow the expense theory

*i*with the smallest absolute difference to the actual rate of expense (

*D*(

*p*,

*p*)). Finally, the firms are classified into the three groups according to the theory that they are implicitly following (units-of-revenue, rate-of-return and compound interest expense theories). The fact that this kind of classification method based on a difference between implied and actual rates is rough should be taken into account when interpreting the results. The hypotheses are tested analyzing differences in

^{i}*IRR*and the revenue lag within and between these groups.

Because the distributions of the parameters do not conform to the normality, non-parametric statistical tests (median tests) are used to test the five research hypotheses. *H1* predicted that the followers of the units-of-revenue expense theory would tend to exhibit average profitability. This hypothesis was tested by the median test to compare the median *IRR* of followers with the median *IRR* of the total sample. *H2* claimed that followers of the rate-of-return expense theory tend to exhibit either positive or negative profitability close to zero, while *H4* predicted that the followers of the compound interest theory would tend to exhibit higher positive or lower negative profitability. These hypotheses were tested by the median tests to compare the absolute values of the median *IRR*s between these groups of followers. *H3* was that followers of the rate-of-return theory tend to exhibit a high revenue lag, and *H5* was that followers of the rate-of-return theory, on the contrary, tend to exhibit a lower revenue lag. These hypotheses were tested by the median tests comparing the estimates of the revenue lag between these groups.

## 4. Empirical results

### 4.1 Descriptive statistics

Table III presents descriptive statistics for the estimation results of growth equations in (25). For the nine-year period (Panel A), growth (*g*) has generally been slow, so that the average annual growth rates for total expenditure and revenue are less than 2 per cent, while the median values slightly exceed this per cent. The lower quartiles of the estimates are negative. The growth rate of total revenue slightly exceeds that of total expenditure, indicating that, on average (at the sample level), the growth process during the period is not steady but that monetary productivity (4) is improving over time. The average weighted growth rate is less than 2 per cent (1.88 per cent). The average coefficients of determination of the growth equations are approximately 50 per cent, but 25 per cent of the cases give a coefficient less than 20 per cent. Therefore, the steady growth path does not always properly explain the actual growth over time.

The parameters estimated for the seven-year period (Panel B) are comparable with those for the longer period, although the average growth rate estimates are somewhat higher, exceeding 2 per cent leading to a weighted rate of 2.27 per cent. At the sample level, however, the average growth rate of total expenditure exceeds that of total revenue, which indicates a reversed (negative) development of monetary productivity as for the longer period. The coefficients of determination for the steady growth models are, on average, little less than for the nine-year period. In general, the effect of growth on the rate of expense (17) for the compound interest theory followers is obviously negligible owing to the low growth estimates. The rate of expense is not sensitive to the rate of growth for these followers (see Appendix 2).

Table IV presents statistics for the parameter estimates of the revenue function (26). For the nine-year period (Panel A), the *t-values* of the estimates for *A* and *q* are quite high, referring to a high stability. The average estimate for *q* is 0.363, which gives an average revenue lag *K* of 0.57 years. The distribution of *IRR* estimates (*r*) is very positively skewed as the average estimate is 0.115, whereas the median values is only 0.039. More than 25 per cent of the sample firms have got a negative estimate for *r*. The revenue–expenditure ratio *F* (5), on average, slightly exceeds unity so that 50 per cent of the observations fall within the range from 0.96-1.05. Therefore, for the majority of firms following the rate-of-return expense theory, the bias in *ROI* (14) is expected to be quite small when approximating *r*. The median of ratio (1 + *g*)/(1 + *r*) is less than unity, but the range is broader than for *F*. Therefore, the bias for the units-of-revenue expense theory in *ROI* (10) can be stronger than for the followers of the rate-of-return expense theory.

The estimates for the longer and shorter periods do not differ remarkably. For the seven-year period, the *t*-statistics are only slightly lower than for the longer period (Panel B). The average estimate for *q* is slightly higher for this period, but the median value is lower. In general, the estimates of *r* are lower for the shorter period. However, in spite of differences in the distributions, the ranges in *F* and (1 + *g*)/(1 + *r*) are comparable referring to a bias of similar height in reporting *ROI*. In general, the differences in the implied rate of expense for followers of different theories can be expected to be small owing to the low estimates of *r.* The lower *r* is, the smaller the differences are in the rate of expense between the followers of different theories (see Appendix 2). If *r* is approaching 0, the differences in the implied rates of expense will also approach 0. For *r = 0*, rates for all three expense theories are equal to 1−*q*.

Table V presents descriptive statistics for the actual and implied rates of expense. For both the nine- (Panel A) and seven-year (Panel B) periods, the average actual rates are about 0.7, and slightly lower for the shorter period. At the level of sample, the medians of the implied rate are a little below those of the actual rate. However, the differences are significantly larger for the mean rates. The distributions of both actual and implied rates are slightly negatively skewed. Table VI presents the coefficients of Spearman rank correlation for the rates of expense. These correlation coefficients are high between the rates of expense from the nine- (Panel A) and seven-year (Panel B) periods. They are also very high (above 0.97) between the different implied rates of expense within the periods, which may be owing to the low rates of *IRR*. However, the rank correlation coefficients between the actual rates and the implied rates are quite low (below 0.30) in both periods, although they are statistically very significant. Thus, at the level of the sample, the association between the actual and implied rates of expense is not strong. This evidence indicates that at the level of the sample, expenses in financial reporting are not directly recognized as matching the accumulation of revenues as described by the revenue lag function.

### 4.2 Classification of sample firms

Table VII presents the industrial distribution of the sample firms by the implied expense theory, classified according to the minimum difference between the actual and implied rates of expense (28). The overall distribution shows that the most frequent implied theory is the rate-of-return expense theory, followed by the majority of firms in both the seven- and nine-year periods (56.7 and 53.4 per cent, respectively). There is also a high frequency of units-of-revenue theory followers (40.9 and 43.6 per cent), but only a few firms followed the compound interest expense theory (2.4 and 3.0 per cent). The industrial distributions for different expense theory followers are quite similar, with manufacturing firms playing the dominant role, followed by wholesale and retail trade firms. The industrial distributions of the sample firms do not statistically differ from each other for the followers of different expense theories in either nine- or seven-year period (two-tailed *p*-values = 0.719 and 0.882, respectively, for the Chi-Square test).

Table VIII presents the distribution of the followers of different theories by legal form, status and accounting practice for the both periods. The frequency distributions are very similar for the private and public limited companies that together form the final sample of firms. However, it is interesting that more than 70 per cent of the cooperative companies (in the initial sample) follow the rate-of-return expense theory. These companies have special objectives and methods to affect reported surplus (and expenses) in comparison with limited companies. However, because of small frequencies of other than limited companies, the legal form is not significantly associated with the implied expense theory in either period (two-tailed *p*-value = 0.163 and 0.821, respectively, for the Chi-Square test). This same conclusion is also valid for the association between the expense theory and the status of the firm (*p*-values = 0.124 and 0.926). It is remarkable that for the shorter period of seven years, the symptoms of financial difficulties (bankruptcy and liquidation) are potentially not yet observable as there is still time, several years, to the event. For the bankrupt firms, the followers of the compound interest theory are exceptionally frequent, which considerably diminishes the *p*-value in Chi-Square test. Similarly, the accounting practice (as observed in the last year) is not significantly associated with the implied expense theory (*p*-value = 0.340 and 0.975).

Table IX presents the frequencies for the transitions of expense theory followers between different theories from the seven- to the nine-year period (in two years). It shows that almost 80 per cent of the units-of-revenue and rate-of-return followers in the seven-year period also follow the same theories in the longer period. In addition, almost 20 per cent of the units-of-revenue theory followers have moved to follow the rate-of-return theory and vice versa. More than 50 per cent of the compound interest theory followers moved to follow units-of-revenue theory and only just over 25 per cent stayed as a compound interest theory follower. Therefore, the evidence indicates that the stability of compound interest theory followers is low, indicating that the borders of the theory are not strong in practice. The transitions between the groups partly replace each other, which means that the cross-sectional distributions are similar in both periods, leading to a strong statistical dependence between them (*p*-value = 0.000 for the chi-square test).

### 4.3 Assessing research hypotheses

Table X presents descriptive statistics of the model variables for different expense theory follower groups. In general, the distributions of the variables are similar for the nine- (Panel A) and seven-year (Panel B) periods. Because the distributions are generally skewed, the medians of the variables characterize the average height of the variables better that the mean. Intuitively, the figures provide support to the present research hypotheses for the longer and shorter periods. First, the medians of *r* for the units-of-revenue expense theory followers (0.062 and 0.059 for the nine- and seven-year periods, respectively) exceed but are close to the median values in the entire sample (0.0386 and 0.0331, respectively), supporting *H1*. However, the *p*-values of Wilcoxon signed rank test when comparing the median of the group with the sample median are 0.263 and 0.018, which indicates that the hypothesis for the seven-year period is to be rejected at *p*-level of 2 per cent. The median of the group of unit-of-revenue theory followers, thus, exceeds the sample median in the shorter period.

Second, the median *IRR* (*r*) is very low for the followers of the rate-of-return expense theory for both periods (0.031 and 0.022), which supports *H2*. These medians are significantly lower than the sample medians (*p*-value = 0.000 and 0.004). For both periods, the mean of *IRR* is slightly negative. The standard deviation of *IRR* is also very low compared with other groups of followers. For this group, the proportion of negative *IRR*s is 32.7 per cent for the nine-year period and 39.1 per cent for the seven-year period. Thus, *IRR*s of this group are concentrated on a narrow range around the origin, which supports *H2*. Third, the median values of *q* are clearly higher (0.423 and 0.398) for the rate-of-return expense theory followers than for the other groups (being less than 0.3). The median value of *q* in this group significantly exceeds the sample median in both periods (*p*-value = 0.000 and 0.000). Thus, the followers of the rate-of-return expense theory tend to exhibit a high revenue lag, consistent with *H3*.

Fourth, the median values of *IRR* are exceptionally high (0.273 and 0.230) for the followers of the compound interest expense theory in both periods. Compared with the median of the rate-of-return theory followers, the median is significantly higher for the nine-year period (two-tailed *p*-value = 0.018), but not for the shorter period (*p*-value = 0.287). In this case, it is not easy to find a statistically significant difference owing to the small number of compound interest expense theory followers (19 and 15). However, the absolute value of *IRR* for this small group is significantly higher than that for the rate-of-return theory followers in both periods (*p*-value = 0.000 and 0.002), which supports *H4*. Fifth, the median values of *q* for this group (0.210 and 0.262, respectively) are clearly lower than for the followers of rate-of-return expense theory (*p*-value = 0.005 and 0.009, respectively), supporting *H5*. Thus, the followers of compound interest expense theory tend to exhibit a lower revenue lag than the rate-of-return theory followers. The median values of (1 + *g*)/(1 + *r*) and *F* are quite close to unity (0.936 and 0.992, respectively), indicating for the units-of-revenue and rate-of-return followers, respectively, that the bias in measuring *IRR* by *ROI* is, on average, not remarkable.

Table XI presents the coefficients of Spearman rank correlation between the model variables and the dummy variables indicating the expense theory followed by a firm. The correlations in both periods are almost identical for the followers of the units-of-revenue theory and the rate-of-return theory, except for the signs of correlation, which are reversed. The lower (higher) that *q*, *g*, (1 + *g*)/(1 + *r*) and *F*, and the higher (lower) *IRR*, the higher likelihood that the firm is a follower of the units-of-revenue (rate-of-return) expense theory. These correlations are all statistically very significant (*p*-value = 0.000). The rank correlations for the followers of the compound interest expense theory are not generally high. The highest correlations (0.196 and 0.145 for the nine-and seven-year periods, respectively) are found for the absolute *IRR* (*p*-value = 0.000). Thus, a follower of the rate-of-return theory can be best identified by an *IRR* close to zero and high *q*, whereas a follower of the compound interest theory is characterized by very high or very low *IRR*. Obviously, the implicit use of the compound interest theory is exceptional. These results support hypotheses *H2*, *H3* and *H4*.

## 5. Concluding discussion

The present study introduces a novel way to consider EM, starting from the expense theories and their implications for financial reporting. It is theoretically based on a steady dynamic model of lagged revenue generation. Thus, the growth rate of the firm is assumed to be constant and the relationships between all variables are considered fixed over time. The model follows the framework of identical investment projects and assumes that periodic total expenditure generates a separate and proportionally identical flow of total revenue that conforms to an infinite geometric lag distribution. Previous studies have used this kind of steady framework to investigate the relationship between *ROI* or *ARR* and *IRR* (Luckett, 1984; Feenstra and Wang, 2000; Brief, 2013). The assumptions of the framework are strict but necessary for modeling different expense theories based on similar separability assumptions. The assumption of the infinite geometric lag function means that the form of the function (average lag) plays the central role in the analysis, while project length (duration) is assumed to be infinite. This assumption simplifies the results significantly and is reasonable owing to the quick convergence of typical geometric lag distributions. It is evident that the set of assumptions describe ideal circumstances that do not exactly hold in reality (Fisher and McGowan, 1983). However, this framework is simple and provides us with a useful tool to investigate the expense theories both analytically and empirically.

The estimation of the model is empirically challenging. Most previous frameworks have been based on modeling the relationship between fixed investments and the lag structure of operating profit. However, this relationship is difficult to estimate empirically as the time-series of investments are usually very instable and do not conform to the steady assumption. The situation is comparable with the difficulties to estimate the rate of depreciation for R&D investments (Hall, 2007, p. 4):

[…] identifying the depreciation rate independently from the return to R&D requires determination of the lag structure of R&D in generating returns. But years of experience with the specification of production functions, market value equations or even patent production functions […] has shown convincingly that this is extremely difficult.

Therefore, the present framework concentrates on the relationship between total expenditure and the lag structure of total revenue. These time-series are steadier and allow the estimation of lag structure in a more reliable way. Thus, the main accounting concept used in this study is (total) expense (and expense theory) instead of depreciation (and depreciation theory).

The steady model is used here to derive the rate of expense for three different expense theories: the units-of-revenue, rate-of-return and compound interest theories. Theoretical analysis indicated first that the use of these theories in financial reporting leads to different *ROI* figures. For the units-of-revenue expense theory, *ROI* depends on the steady growth rate in addition to *IRR*, while for the rate-of-return expense theory, it also depends on the revenue lag. The use of compound interest theory exactly leads to *ROI* = *IRR* without any bias, as Vatter (1966) also concluded. These results are in line with the conclusion of Feenstra and Wang (2000, p. 18):

It seems clear that because of the different choice of accounting methods ARR can be viewed as a surrogate measure of IRR that will contain a measurement error in most settings.

Second, theoretical analysis indicated that the use of the units-of-revenue expense theory leads to a rate of expense that only depends on the revenue lag acting as a benchmark for timing of expenses. For the rate-of-return expense theory, the resulted rate of return depends on *IRR* in addition to the revenue lag; for the compound interest theory, it is further influenced by growth as well. Thus, a different choice of expense methods in reporting results in different rates of expense.

The theoretical model made it possible to draw five hypotheses for the empirical part. First, I assumed that the units-of-revenue theory represents a neutral expense method and therefore expected that the followers of this theory exhibit an average profitability (*H1*) without any pressure for smoothing. The rate-of-interest theory and the compound interest theory both include a smoothing mechanism in which the rates of expense are higher than the neutral rate for profitable firms and lower for unprofitable firms. This smoothing mechanism is stronger for the rate-of-interest theory than for the compound interest theory, where the rate of expense also depends on growth. The last four hypotheses were drawn for these theories, assuming flexibility limits for smoothing. These limits vary with changes in the legal and business environment (Choy, 2012). The present concepts make the limits narrow. In general, the major part of expenditures is current expiring within the accounting period. Therefore, the flexibility limits, as a percentage of the neutral rate of expense, are expected to be quite narrow. Narrow limits may seriously constrain smoothing in practice. Barton and Simko (2002) suggested that firms with low flexibility have difficulty managing earnings up by even 1 cent per share to meet the forecasts given by analysts. For narrow limits, *IRR* of rate-of-return theory followers are expected to concentrate on a narrow area around the origin (*H2*) while the revenue lag is expected to be high (*H3*). However, the followers of the compound interest theory are expected to exhibit higher *IRR* (*H4*) and lower revenue lag (*H5*).

The present empirical analysis is based on nine-year time-series data from 1,015 Finnish firms that each employ more than 50 people. The parameters of the steady model of revenue generation were estimated by the ordinary (growth) and restricted (*IRR* and the revenue lag) LS (RLS) methods. Empirical tests showed that the RLS method significantly diminishes the variance of the estimates, leading to more reliable results than the OLS method when estimating *IRR* and the revenue lag. However, because of the instability of the firm-level time-series, the per cent of inconsistent estimates was not negligible, emphasizing the difficulty of lagged revenue function estimation (Hall, 2007). The parameters were estimated for the available nine years, but also for the first seven years to assess the robustness of the results and to investigate the structural change in the last years. In general, the parameters for the periods were consistent with each other. Thus, it can be concluded that even time-series of seven years can be sufficient for estimating a revenue lag function for a firm.

The final sample (631 firms) was significantly smaller than the original one as the statistical analysis was only applied to active limited companies with consistent estimates. In Finland, the research period was characterized by strong negative economic development. Therefore, the average growth rate and *IRR* were low and one-third of the sample firms exhibited negative long-term growth (32.3 per cent) or profitability (33.3 per cent). This kind of development provided us with an opportunity to analyze reporting behavior of firms in very different circumstances. However, it also led to the differences in the rate of expense implied by different theories being small, on average and quite difficult to identify directly from observations. Therefore, the results are rough and should be interpreted cautiously. For the 10-year period, the analyses pointed out that 43.6 per cent of the sample firms can be regarded as followers of the units-of-revenue expense theory exhibiting a neutral rate of expense. However, 53.4 per cent of the firms follow the rate-of-return theory reporting a smoothed rate. The compound interest theory has only few followers (3.0 per cent) consistently with expectations (Bragg, 2010). These figures are consistent with those reported by Burgstahler and Dichev (1997) for the popularity of EM. In general, expenses in financial reporting were not directly recognized as matching very closely the accumulation of revenues.

The firms following different expense theories were statistically distributed between industries and between accounting practices (GAAP or IFRS) in a similar way. Thus, the choice to follow a theory does not obviously depend on industry or accounting practice. However, the followers of the units-of-revenue theory were more frequent among cooperative companies than among other legal forms, emphasizing differences in smoothing between limited and cooperative companies. The transition of different expense theory followers between theories in the research periods was quite rare for the followers of units-of-revenue and rate-of-interest theories as almost 80 per cent of them did not move to another theory. However, only about one-fourth of the compound interest theory followers maintained their theory during the both periods. This strong movement from and to the followers of the theory reveals that the domain of the theory is not stable and strictly separated from the domain of other theories.

Statistical analyses confirmed the research hypotheses. The followers of the units-of-revenue theory tend to exhibit quite average *IRR* and revenue lag. However, the *IRR*s of the rate-of-return theory followers are concentrated around the origin, while the average revenue lag is high. The followers of the compound interest theory exhibit exceptionally high and low figures for *IRR*, but the revenue lag is moderately low. As this theory is followed by firms exhibiting exceptional values of *IRR*, it is rare in practice and the domain is unstable as quick changes in time are characteristic for exceptional values. Therefore, it seems that business firms can roughly be classified as those in which the expiration of expenditure roughly follows the accumulation of revenue and those in which the reported figures are smoothed in relation to (positive or negative) long-term profitability. The higher the *IRR,* and lower the revenue lag, the higher the likelihood that the firm belongs to the former group. Those firms exhibiting exceptionally high or low *IRR* cannot fully use the smoothing mechanism of the rate-of-return theory followers and, owing to flexibility limits, cut its smoothing efficiency in relation to the revenue lag. Further analyses indicated that the likelihood of belonging to any of the three groups is not strongly associated with average financial ratios, bankruptcy risk or change in the bankruptcy risk (Appendix 3). It is noteworthy that the reported *ROI* figures are biased for the units-of-revenue and rate-of-return theory followers. However, the average bias is not strong owing to low average *IRR* and growth rate.

This study provides a number of implications that can be summarized as follows. First, more than 40 per cent of Finnish firms are roughly identified as followers of a neutral expense theory, while more than 50 per cent follow a theory including a smoothing mechanism. The compound interest theory, which includes a strong smoothing mechanism and leads to correct *ROI* (*IRR*), has only few followers with extreme profitability. Therefore, it appears to be an expense method without any significant practical value. Second, when compared with *IRR*, the reported *ROI* ratios are biased for the majority of firms. However, the bias may be quite small because of low average growth and profitability. Third, the frequencies of the followers of the theories were similar for all types of firms except for the cooperative firms, which mainly followed the rate-of-return expense theory. Fourth, in spite of its strict assumptions, the approach proved to be a promising method of assessing EM. Fifth, the estimation of the lagged revenue distribution can be successful when using a restricted estimation method. However, only 62 per cent of the cases (firms) fulfilled all logical restrictions set for the estimates. Therefore, the properties of both the underlying model and the estimation method should be improved.

In summary, the present study introduced a new approach to analyze financial reporting based on different theories of expense and the implied behavior of business firms. The findings of this study are rough and exposed to certain limitations and should, therefore, be considered preliminary and interpreted cautiously. The framework behind the analysis is a long-term steady model of lagged revenue generation based on many simplifying assumptions on constant growth and infinite lag function. The research period in Finland was economically very difficult, making many firm-level time-series unstable, which made the estimation of growth and revenue function a very challenging task. Therefore, the estimation results and followed interpretations are rough and inaccurate. Future studies should develop new statistical methods to solve these difficult estimation problems, as outlined by Hall (2007). The present study concentrated on the rate of total expense to facilitate estimation at the level of firm. Consequently, familiar depreciation methods were excluded from the analysis. New methods should be developed to analyze the effects of different depreciation methods, such as the straight-line method, sum of years’ digits method and declining balance depreciation for a finite project length.

## Figures

The number of employees in the original sample firms in each year

Year | Minimum | Maximum | Mean | Median | SD | Skewness | Kurtosis |
---|---|---|---|---|---|---|---|

Last year (t) |
50 | 61,656 | 893.83 | 204 | 3,363.12 | 10.836 | 155.467 |

t-1 |
51 | 55,244 | 907.57 | 207 | 3,337.68 | 9.606 | 118.109 |

t-2 |
50 | 65,547 | 936.15 | 204 | 3,532.28 | 10.309 | 142.941 |

t-3 |
50 | 130,050 | 1,013.09 | 202 | 5,022.67 | 18.272 | 437.408 |

t-4 |
50 | 132,427 | 970.47 | 196 | 4,973.54 | 19.520 | 487.705 |

t-5 | 50 | 123,553 | 973.60 | 202 | 4,776.12 | 18.197 | 435.271 |

t-6 |
50 | 125,829 | 1,113.45 | 210 | 5,800.51 | 15.430 | 291.242 |

t-7 |
52 | 112,262 | 1,001.86 | 210 | 4,596.89 | 16.074 | 350.176 |

t-8 |
50 | 684,83 | 918.08 | 190 | 3,682.34 | 10.653 | 149.257 |

t-9 |
50 | 588,74 | 885.64 | 178 | 3,519.03 | 9.789 | 120.366 |

Fulfillment of predetermined criteria in the original sample (N = 1,015)

Criterion | Firms fulfilling | Firms not fulfilling | ||
---|---|---|---|---|

Number | (%) | Number | (%) | |

Panel A. Nine years |
||||

1. q/(1 + r) < 1 |
947 | 93.30 | 68 | 6.70 |

2. r > −1 |
900 | 88.67 | 115 | 11.33 |

3. r< 3 |
944 | 93.00 | 71 | 7.00 |

4. q< 1 |
935 | 92.12 | 80 | 7.88 |

5. q> 0 |
891 | 87.78 | 124 | 12.22 |

6. g< 1 |
935 | 92.12 | 80 | 7.88 |

7. g < −1 |
956 | 94.19 | 59 | 5.81 |

Panel B. Seven years |
||||

8. q/(1 + r) < 1 |
922 | 90.84 | 93 | 9.16 |

9. r > −1 |
914 | 90.05 | 101 | 9.95 |

10. r< 3 |
955 | 94.09 | 60 | 5.91 |

11. q< 1 |
905 | 89.16 | 110 | 10.84 |

12. q> 0 |
870 | 85.71 | 145 | 14.29 |

13. g< 1 |
914 | 90.05 | 101 | 9.95 |

14. g < −1 |
959 | 94.48 | 56 | 5.52 |

Panel C. Firm-level criteria |
||||

15. Firm is an industrial company | 971 | 95.67 | 44 | 4.33 |

16. Firm is a limited company | 986 | 97.14 | 29 | 2.86 |

17. Firm is an active company | 950 | 93.60 | 65 | 6.40 |

Average | 932.59 | 91.88 | 82.41 | 8.12 |

Panel 2. Number of criteria fulfilled by the sample firms |
||

No. of criteria | Firms fulfilling: | |

No. | (%) | |

2 | 10 | 0.99 |

3 | 36 | 3.55 |

5 | 1 | 0.10 |

10 | 4 | 0.39 |

11 | 14 | 1.38 |

12 | 6 | 0.59 |

13 | 28 | 2.76 |

14 | 37 | 3.65 |

15 | 122 | 12.02 |

16 | 126 | 12.41 |

17 | 631 | 62.17 |

Final sample | 631 | 62.17 |

Original sample | 1,015 | 100.00 |

Descriptive statistics of the steady growth estimates (*N* = 631)

Percentile | |||||
---|---|---|---|---|---|

Estimate | Mean | SD | 25 | 50 | 75 |

Panel A. Nine years |
|||||

g (total revenue) |
0.0190 | 0.0594 | −0.0120 | 0.0211 | 0.0511 |

R^{2} (total revenue) |
0.4975 | 0.3213 | 0.1912 | 0.5563 | 0.7915 |

g (total expenditure) |
0.0187 | 0.0602 | −0.0118 | 0.0205 | 0.0512 |

R^{2} (total expenditure) |
0.4416 | 0.3139 | 0.1418 | 0.4335 | 0.7242 |

g (weighted average) |
0.0188 | 0.0591 | −0.0112 | 0.0197 | 0.0506 |

Panel B. Seven years |
|||||

g (total revenue) |
0.0222 | 0.0692 | −0.0121 | 0.0215 | 0.0581 |

R^{2} (total revenue) |
0.4894 | 0.3294 | 0.1641 | 0.5173 | 0.8054 |

g (total expenditure) |
0.0234 | 0.0696 | −0.0113 | 0.0227 | 0.0577 |

R^{2} (total expenditure) |
0.4345 | 0.3220 | 0.1335 | 0.4079 | 0.7281 |

g (weighted average) |
0.0227 | 0.0683 | −0.0127 | 0.0214 | 0.0571 |

Descriptive statistics of the steady revenue function estimates (*N* = 631)

Percentile | |||||
---|---|---|---|---|---|

Estimate | Mean | SD | 25 | 50 | 75 |

Panel A. Nine years |
|||||

A |
0.6524 | 0.2321 | 0.5014 | 0.6972 | 0.8483 |

T-statistics |
9.4077 | 8.8990 | 4.1189 | 7.2116 | 12.0197 |

q |
0.3630 | 0.2385 | 0.1679 | 0.3216 | 0.5226 |

T-statistics |
4.3920 | 4.4606 | 1.9266 | 3.2561 | 5.3861 |

r |
0.1152 | 0.3955 | −0.0258 | 0.0386 | 0.1409 |

F |
1.0151 | 0.1005 | 0.9635 | 1.0074 | 1.0515 |

(1 + g)/(1 + r) |
1.0089 | 0.4744 | 0.8724 | 0.9870 | 1.0662 |

Panel B. Seven years |
|||||

A |
0.6364 | 0.2486 | 0.4602 | 0.7002 | 0.8437 |

T-statistics |
9.7984 | 15.5699 | 3.4039 | 6.7579 | 11.2049 |

q |
0.3742 | 0.2598 | 0.1613 | 0.3040 | 0.5525 |

T-statistics |
4.3199 | 4.6823 | 1.6853 | 3.0146 | 5.3974 |

r |
0.0811 | 0.3882 | −0.0555 | 0.0331 | 0.1195 |

F |
1.0008 | 0.1126 | 0.9465 | 0.9943 | 1.0412 |

(1 + g)/(1 + r) |
1.0876 | 0.9361 | 0.8938 | 1.0075 | 1.0977 |

Descriptive statistics of the actual and implied rates of expense (*N* = 631)

Percentile | |||||
---|---|---|---|---|---|

Estimate | Mean | St. Dev. | 25 | 50 | 75 |

Panel A. Nine-year period |
|||||

p (actual rate) |
0.7057 | 0.1500 | 0.6202 | 0.7140 | 0.8087 |

p^{p} (units-of-revenue theory) |
0.6370 | 0.2385 | 0.4774 | 0.6784 | 0.8321 |

p^{r} (rate-of-return theory) |
0.6524 | 0.2321 | 0.5014 | 0.6972 | 0.8483 |

p^{a} (compound interest theory) |
0.6460 | 0.2382 | 0.4815 | 0.6987 | 0.8460 |

Panel B. Seven-year period |
|||||

p (actual rate) |
0.6955 | 0.1514 | 0.6098 | 0.7080 | 0.7954 |

p^{p} (units-of-revenue theory) |
0.6258 | 0.2598 | 0.4475 | 0.6960 | 0.8387 |

p^{r} (rate-of-return theory) |
0.6364 | 0.2486 | 0.4602 | 0.7002 | 0.8437 |

p^{a} (compound interest theory) |
0.6303 | 0.2574 | 0.4452 | 0.7013 | 0.8403 |

Spearman rank correlation coefficients (all significant at the 0.01 level) (*N* = 631)

Nine-year period | Seven-year period | |||||||
---|---|---|---|---|---|---|---|---|

Estimate | p |
p^{p} |
p^{r} |
p^{a} |
p |
p^{p} |
p^{r} |
p^{a} |

Panel A. Nine-year period |
||||||||

p (actual rate) |
1.000 | 0.257 | 0.269 | 0.265 | 0.983 | 0.222 | 0.241 | 0.234 |

p^{p} (units-of-revenue theory) |
0.257 | 1.000 | 0.977 | 0.986 | 0.252 | 0.877 | 0.842 | 0.852 |

p^{r} (rate-of-return theory) |
0.269 | 0.977 | 1.000 | 0.998 | 0.262 | 0.863 | 0.871 | 0.873 |

p^{a} (compound interest theory) |
0.265 | 0.986 | 0.998 | 1.000 | 0.258 | 0.869 | 0.867 | 0.872 |

Panel B. Seven-year period |
||||||||

p (actual rate) |
0.983 | 0.252 | 0.262 | 0.258 | 1.000 | 0.237 | 0.264 | 0.255 |

p^{p} (units-of-revenue theory) |
0.222 | 0.877 | 0.863 | 0.869 | 0.237 | 1.000 | 0.970 | 0.980 |

p^{r} (rate-of-return theory) |
0.241 | 0.842 | 0.871 | 0.867 | 0.264 | 0.970 | 1.000 | 0.998 |

p^{a} (compound interest theory) |
0.234 | 0.852 | 0.873 | 0.872 | 0.255 | 0.980 | 0.998 | 1.000 |

Distribution of different implied expense theory followers by industry (*N* = 631)

Nine-year period | Seven-year period | |||||
---|---|---|---|---|---|---|

Units-of-revenue | Rate-of-return | Compound interest | Units-of-revenue | Rate-of-return | Compound interest | |

NACE classification | (%) | (%) | (%) | (%) | (%) | (%) |

A Agriculture, forestry and fishing | 0.36 | 0.89 | 0.00 | 0.39 | 0.84 | 0.00 |

C Manufacturing | 41.09 | 38.58 | 36.84 | 42.25 | 37.43 | 46.67 |

D Electricity, gas, steam and air conditioning supply | 2.18 | 1.48 | 0.00 | 1.55 | 1.96 | 0.00 |

E Water supply; sewerage, waste management | 0.73 | 0.59 | 0.00 | 0.78 | 0.56 | 0.00 |

F Construction | 4.36 | 8.01 | 10.53 | 5.43 | 7.26 | 6.67 |

G Wholesale and retail trade | 23.64 | 16.02 | 21.05 | 22.48 | 17.04 | 26.67 |

H Transportation and storage | 6.18 | 6.82 | 0.00 | 5.04 | 7.26 | 6.67 |

I Accommodation and food service activities | 2.18 | 3.56 | 10.53 | 1.94 | 4.19 | 0.00 |

J Information and communication | 6.18 | 5.93 | 10.53 | 6.59 | 5.87 | 6.67 |

K Financial and insurance activities | 3.27 | 2.37 | 5.26 | 3.88 | 2.23 | 0.00 |

M Professional, scientific and technical activities | 5.45 | 8.31 | 5.26 | 5.81 | 7.82 | 6.67 |

N Administrative and support service activities | 1.82 | 4.15 | 0.00 | 1.55 | 4.19 | 0.00 |

P Education | 0.00 | 0.30 | 0.00 | 0.00 | 0.28 | 0.00 |

Q Human health and social work activities | 0.36 | 0.59 | 0.00 | 0.00 | 0.84 | 0.00 |

R Arts, entertainment and recreation | 1.45 | 0.89 | 0.00 | 1.55 | 0.84 | 0.00 |

S Other service activities | 0.73 | 1.48 | 0.00 | 0.78 | 1.40 | 0.00 |

Total | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |

Number of firms | 275 | 337 | 19 | 258 | 358 | 15 |

Per cent of firms | 43.58 | 53.41 | 3.01 | 40.89 | 56.74 | 2.38 |

Distribution of different implied expense theory followers by legal form, status and accounting practice

Nine-year period | Seven-year period | ||||||
---|---|---|---|---|---|---|---|

Units-of-revenue | Rate-of-return | Compound interest | Units-of-revenue | Rate-of-return | Compound interest | No. of firms | |

Firm characteristic | (%) | (%) | (%) | (%) | % | (%) | |

Panel A. Legal form |
|||||||

Cooperative company | 20.83 | 79.17 | 0.00 | 29.17 | 70.83 | 0.00 | 24 |

Foundation | 0.00 | 100.00 | 0.00 | 0.00 | 100.00 | 0.00 | 1 |

Limited partnership | 0.00 | 100.00 | 0.00 | 0.00 | 100.00 | 0.00 | 1 |

Private limited company | 42.62 | 54.10 | 3.28 | 40.44 | 57.19 | 2.37 | 549 |

Public limited company | 50.00 | 48.78 | 1.22 | 43.90 | 53.66 | 2.44 | 82 |

Panel B. Status |
|||||||

Active | 43.58 | 53.41 | 3.01 | 40.89 | 56.74 | 2.38 | 631 |

Active (insolvency procedure) | 0.00 | 100.00 | 0.00 | 0.00 | 100.00 | 0.00 | 1 |

Bankruptcy | 57.14 | 14.29 | 28.57 | 42.86 | 57.14 | 0.00 | 7 |

Dissolved | 52.50 | 42.50 | 5.00 | 39.02 | 56.10 | 4.88 | 40 |

Dissolved (merger or take-over) | 50.00 | 50.00 | 0.00 | 0.00 | 100.00 | 0.00 | 2 |

Panel C. Accounting practice (last year) |
|||||||

IFRS | 50.68 | 47.95 | 1.37 | 41.10 | 56.16 | 2.74 | 73 |

Local GAAP | 42.65 | 54.12 | 3.23 | 40.86 | 56.81 | 2.33 | 558 |

Transition of expense theory followers between different theories (*N* = 631)

Expense theory (nine years) | ||||
---|---|---|---|---|

Expense theory (seven years) | Units-of-revenue | Rate-of-return | Compound interest | Total |

Panel A. Frequency distribution |
||||

Units-of-revenue theory | 201 | 48 | 9 | 258 |

Rate-of-return theory | 66 | 286 | 6 | 358 |

Compound interest theory | 8 | 3 | 4 | 15 |

Total | 275 | 337 | 19 | 631 |

Panel B. Percentage distribution |
||||

Units-of-revenue theory | 77.91 | 18.60 | 3.49 | 100.00 |

Rate-of-return theory | 18.44 | 79.89 | 1.68 | 100.00 |

Compound interest theory | 53.33 | 20.00 | 26.67 | 100.00 |

Descriptive statistics of the model variables for different expense theory followers (*N* = 631)

Expense theory followed by firms: | |||||||||
---|---|---|---|---|---|---|---|---|---|

Units-of-revenue theory | Rate-of-return theory | Compound interest theory | |||||||

Estimate | Mean | Std. dev. | Median | Mean | SD. | Median | Mean | Std. dev. | Median |

Panel A. Nine-year period |
|||||||||

A |
0.731 | 0.204 | 0.783 | 0.579 | 0.233 | 0.594 | 0.809 | 0.123 | 0.833 |

q |
0.284 | 0.188 | 0.238 | 0.434 | 0.256 | 0.423 | 0.240 | 0.151 | 0.210 |

r |
0.233 | 0.478 | 0.062 | −0.004 | 0.183 | 0.031 | 0.534 | 0.839 | 0.273 |

Absolute r | 0.275 | 0.455 | 0.100 | 0.120 | 0.139 | 0.073 | 0.668 | 0.730 | 0.372 |

g (weighted) | 0.009 | 0.058 | 0.011 | 0.029 | 0.056 | 0.031 | −0.012 | 0.089 | 0.014 |

F |
1.017 | 0.071 | 1.017 | 1.010 | 0.117 | 0.992 | 1.083 | 0.119 | 1.056 |

(1 + g)/(1 + r) |
0.895 | 0.231 | 0.936 | 1.113 | 0.588 | 1.010 | 0.819 | 0.397 | 0.812 |

Number of firms | 275 | 337 | 19 | ||||||

Per cent of negative r (%) | 34.55 | 32.94 | 21.05 | ||||||

Panel B. Seven-year period |
|||||||||

A |
0.724 | 0.208 | 0.772 | 0.569 | 0.259 | 0.602 | 0.740 | 0.110 | 0.708 |

Q |
0.289 | 0.189 | 0.250 | 0.439 | 0.288 | 0.398 | 0.285 | 0.100 | 0.262 |

R |
0.222 | 0.483 | 0.059 | −0.027 | 0.250 | 0.022 | 0.226 | 0.469 | 0.230 |

Absolute r | 0.276 | 0.455 | 0.116 | 0.147 | 0.203 | 0.078 | 0.372 | 0.355 | 0.287 |

g (weighted) |
0.010 | 0.067 | 0.010 | 0.033 | 0.066 | 0.034 | −0.009 | 0.086 | −0.001 |

F |
1.008 | 0.080 | 1.014 | 0.993 | 0.129 | 0.981 | 1.051 | 0.159 | 1.064 |

(1 + g)/(1 + r) |
0.911 | 0.261 | 0.943 | 1.221 | 1.204 | 1.025 | 0.928 | 0.383 | 0.850 |

Number of firms | 258 | 358 | 15 | ||||||

Per cent of negative r (%) |
37.98 | 39.11 | 33.33 |

Spearman rank correlation coefficients between follower dummies and model variables

Nine-year period | Seven-year period | |||||
---|---|---|---|---|---|---|

Dummy variable for the followers of | Dummy variable for the followers of | |||||

Variable | Units-of-revenue | Rate-of-return | Compound interest | Units-of-revenue | Rate-of-return | Compound interest |

A |
0.309 | −0.348 | 0.121 | 0.291 | −0.303 | 0.048 |

p-value |
(0.000) |
(0.000) |
(0.002) |
(0.000) |
(0.000) |
(0.230) |

q |
−0.273 | 0.302 | −0.089 | −0.234 | 0.241 | −0.028 |

p-value |
(0.000) |
(0.000) |
(0.026) |
(0.000) | (0.000) | (0.484) |

r |
0.208 | −0.247 | 0.119 | 0.249 | −0.267 | 0.066 |

p-value |
(0.000) |
(0.000) |
(0.003) |
(0.000) |
(0.000) |
(0.100) |

Absolute r |
0.099 | −0.165 | 0.196 | 0.076 | −0.121 | 0.145 |

p-value |
(0.013) |
(0.000) |
(0.000) |
(0.055) | (0.002) | (0.000) |

g (weighted) |
−0.192 | 0.210 | −0.055 | −0.189 | 0.203 | −0.050 |

p-value |
(0.000) |
(0.000) |
(0.168) |
(0.000) |
(0.000) |
(0.207) |

F |
0.110 | −0.151 | 0.120 | 0.170 | −0.188 | 0.063 |

p-value |
(0.006) |
(0.000) |
(0.003) |
(0.000) | (0.000) | (0.115) |

(1 + g)/(1 + r) |
−0.281 | 0.320 | −0.121 | −0.305 | 0.322 | −0.064 |

p-value |
(0.000) |
(0.000) |
(0.002) |
(0.000) |
(0.000) |
(0.109) |

Two-tailed significance (*p*-value)

Macroeconomic figures of Finland in years 2003-2014

Year: | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Variable | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 |

Bankruptcy risk (%) | 1.21 | 1.05 | 0.96 | 0.91 | 0.73 | 0.81 | 1.02 | 0.9 | 0.91 | 0.92 | 0.95 | 0.81 |

Number of bankruptcies | 2769 | 2428 | 2278 | 2285 | 2254 | 2612 | 3275 | 2864 | 2947 | 2961 | 3131 | 2954 |

Change (%) in Gross domestic product (GDP) | 2.0 | 3.9 | 2.8 | 4.1 | 5.2 | 0.7 | −8.3 | 3.0 | 2.6 | −1.4 | −0.8 | −0.7 |

Industrial confidence indicator, Finland | −2.0 | 6.9 | 7.6 | 19.6 | 15.9 | −33.3 | −8.9 | 11.2 | −8.8 | −13.7 | −6.1 | −8.2 |

Industrial confidence indicator, Euro area | −7.2 | −2.6 | −3.7 | 6.8 | 3.0 | −32.9 | −16.2 | 5.1 | −6.9 | −13.5 | −2.9 | −5.0 |

Change (%) in wage level index | 4.0 | 3.8 | 3.9 | 2.9 | 3.4 | 5.5 | 4.0 | 2.6 | 2.7 | 3.2 | 2.1 | 1.4 |

Change (%) in consumer price level | 0.9 | 0.2 | 0.9 | 1.6 | 2.5 | 4.1 | 0.0 | 1.2 | 3.4 | 2.8 | 1.5 | 0.5 |

Unemployment rate (%) | 9.0 | 8.8 | 8.4 | 7.7 | 6.9 | 6.4 | 8.2 | 8.4 | 7.8 | 7.7 | 8.2 | 8.7 |

Government bond interest rate, 5 years | 3.28 | 3.25 | 2.85 | 3.59 | 4.18 | 3.88 | 2.7 | 1.78 | 2.08 | 0.87 | 0.81 | 0.51 |

Government bond interest rate, 10 years | 4.13 | 4.11 | 3.35 | 3.78 | 4.29 | 4.3 | 3.74 | 3.00 | 3.00 | 1.89 | 1.86 | 1.44 |

Government bond reference interest rate, Euro area, 10 years | 4.16 | 4.14 | 3.44 | 3.86 | 4.33 | 4.23 | 3.81 | 3.13 | 3.15 | 2.14 | 1.96 | 1.35 |

Examples of the rate of expense for different expense theories

r = −0.05 |
r = 0.05 |
r = 0.15 |
|||||||
---|---|---|---|---|---|---|---|---|---|

Q |
Units-of-revenue | Rate-of-return | Compound interest | Units-of-revenue | Rate-of-return | Compound interest | Units-of-revenue | Rate-of-return | Compound interest |

Panel 1. g = −0.05 |
|||||||||

q= 0.20 |
0.800 | 0.789 | 0.792 | 0.800 | 0.810 | 0.808 | 0.800 | 0.826 | 0.821 |

q= 0.30 |
0.700 | 0.684 | 0.689 | 0.700 | 0.714 | 0.710 | 0.700 | 0.739 | 0.728 |

q= 0.40 |
0.600 | 0.579 | 0.588 | 0.600 | 0.619 | 0.611 | 0.600 | 0.652 | 0.632 |

q= 0.50 |
0.500 | 0.474 | 0.488 | 0.500 | 0.524 | 0.512 | 0.500 | 0.565 | 0.533 |

Panel 2. g = 0.00 |
|||||||||

q= 0.20 |
0.800 | 0.789 | 0.792 | 0.800 | 0.810 | 0.808 | 0.800 | 0.826 | 0.821 |

q= 0.30 |
0.700 | 0.684 | 0.689 | 0.700 | 0.714 | 0.710 | 0.700 | 0.739 | 0.729 |

q= 0.40 |
0.600 | 0.579 | 0.588 | 0.600 | 0.619 | 0.612 | 0.600 | 0.652 | 0.633 |

q= 0.50 |
0.500 | 0.474 | 0.487 | 0.500 | 0.524 | 0.512 | 0.500 | 0.565 | 0.535 |

Panel 3. g = 0.05 |
|||||||||

q= 0.20 |
0.800 | 0.789 | 0.792 | 0.800 | 0.810 | 0.808 | 0.800 | 0.826 | 0.822 |

q= 0.30 |
0.700 | 0.684 | 0.689 | 0.700 | 0.714 | 0.710 | 0.700 | 0.739 | 0.729 |

q= 0.40 |
0.600 | 0.579 | 0.587 | 0.600 | 0.619 | 0.612 | 0.600 | 0.652 | 0.634 |

q= 0.50 |
0.500 | 0.474 | 0.487 | 0.500 | 0.524 | 0.513 | 0.500 | 0.565 | 0.536 |

Panel 4. g = 0.10 |
|||||||||

q= 0.20 |
0.800 | 0.789 | 0.791 | 0.800 | 0.810 | 0.808 | 0.800 | 0.826 | 0.822 |

q= 0.30 |
0.700 | 0.684 | 0.689 | 0.700 | 0.714 | 0.711 | 0.700 | 0.739 | 0.730 |

q= 0.40 |
0.600 | 0.579 | 0.587 | 0.600 | 0.619 | 0.612 | 0.600 | 0.652 | 0.635 |

q= 0.50 |
0.500 | 0.474 | 0.486 | 0.500 | 0.524 | 0.513 | 0.500 | 0.565 | 0.538 |

## Appendix 1

## Appendix 2

## Appendix 3

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## Further reading

Eckel, N. (1981), “The income smoothing hypothesis revisited”, Abacus, Vol. 17 No. 1, pp. 28-40.

## About the author

Erkki Kalervo Laitinen, Department of Accounting and Business Finance, University of Vaasa, P.O. Box 700, FI-65101 Vaasa, Finland. Erkki Kalervo Laitinen is an Emeritus Professor of Accounting at the University of Vaasa, Finland. He obtained his PhD at the University of Jyväskylä in 1980 and taught at the same university and at the Lappeenranta University of Technology before joining the University of Vaasa in 1987. He has published several textbooks and a large number of scientific articles including in the *Journal of Business Finance and Accounting*, *Management Accounting Research*, *Long Range Planning*, *International Small Business Journal*, *Scandinavian Journal of Management*, *Journal of International Review of Financial Analysis*, *International Journal of Management Science (Omega)*, *European Journal of Operational Research*, *The European Accounting Review*, *Accounting, Auditing & Accountability Journal*, *Review of Accounting and Finance*, *International Journal of Accounting*, *Auditing and Performance Evaluation*, *The Finnish Journal of Business Economics and Critical Perspectives on Accounting*.